modern financial management solutions manual

8/11/2019 Modern Financial Management Solutions Manual

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End of Chapter SolutionsModern Financial Management8thedition

Ross, Westerfield, Jaffe, Jordan


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CHAPTER 1

INTRODUCTION TO CORPORATE

FINANCE

Answers to Concept Questions

1. In the corporate form of ownership, the shareholders are the owners of the firm. The shareholderselect the directors of the corporation, who in turn appoint the firms management. This separation ofownership from control in the corporate form of organiation is what causes agenc! pro"lems toe#ist. $anagement ma! act in its own or someone elses "est interests, rather than those of theshareholders. If such e%ents occur, the! ma! contradict the goal of ma#imiing the share price of thee&uit! of the firm.

2. Such organiations fre&uentl! pursue social or political missions, so man! different goals areconcei%a"le. 'ne goal that is often cited is re%enue minimiation( i.e., pro%ide whate%er goods andser%ices are offered at the lowest possi"le cost to societ!. ) "etter approach might "e to o"ser%e thate%en a not*for*profit "usiness has e&uit!. Thus, one answer is that the appropriate goal is toma#imie the %alue of the e&uit!.

3. +resuma"l!, the current stoc %alue reflects the ris, timing, and magnitude of all future cash flows,"oth short*term andlong*term. If this is correct, then the statement is false.

4. )n argument can "e made either wa!. )t the one e#treme, we could argue that in a maret econom!,all of these things are priced. There is thus an optimal le%el of, for e#ample, ethical and-or illegal"eha%ior, and the framewor of stoc %aluation e#plicitl! includes these. )t the other e#treme, wecould argue that these are non*economic phenomena and are "est handled through the politicalprocess. ) classic and highl! rele%ant/ thought &uestion that illustrates this de"ate goes somethinglie this0 1) firm has estimated that the cost of impro%ing the safet! of one of its products is 234million. 5owe%er, the firm "elie%es that impro%ing the safet! of the product will onl! sa%e 264million in product lia"ilit! claims. What should the firm do7

5. The goal will "e the same, "ut the "est course of action toward that goal ma! "e different "ecause ofdiffering social, political, and economic institutions.

6. The goal of management should "e to ma#imie the share price for the current shareholders. Ifmanagement "elie%es that it can impro%e the profita"ilit! of the firm so that the share price wille#ceed 239, then the! should fight the offer from the outside compan!. If management "elie%es that

this "idder or other unidentified "idders will actuall! pa! more than 239 per share to ac&uire thecompan!, then the! should still fight the offer. 5owe%er, if the current management cannot increasethe %alue of the firm "e!ond the "id price, and no other higher "ids come in, then management is notacting in the interests of the shareholders "! fighting the offer. Since current managers often losetheir :o"s when the corporation is ac&uired, poorl! monitored managers ha%e an incenti%e to fightcorporate taeo%ers in situations such as this.


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SOLUTIONS

7. We would e#pect agenc! pro"lems to "e less se%ere in other countries, primaril! due to the relati%el!small percentage of indi%idual ownership. ;ewer indi%idual owners should reduce the num"er ofdi%erse opinions concerning corporate goals. The high percentage of institutional ownership mightlead to a higher degree of agreement "etween owners and managers on decisions concerning ris!pro:ects. In addition, institutions ma! "e "etter a"le to implement effecti%e monitoring mechanismson managers than can indi%idual owners, "ased on the institutions deeper resources and e#periences

with their own management.

8. The increase in institutional ownership of stoc in the 44 toda! when the

share price in one !ear is e#pected to "e =847

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CHAPTER 2

FINANCIAL STATEMENTS AND CASHFLOW

Answers to Concepts Review and Critical !in"in# Questions

1. True. E%er! asset can "e con%erted to cash at some price. 5owe%er, when we are referring to a li&uidasset, the added assumption that the asset can "e con%erted cash at or near maret %alue is important.

2. The recognition and matching principles in financial accounting call for re%enues, and the costsassociated with producing those re%enues, to "e 1"ooed when the re%enue process is essentiall!complete, not necessaril! when the cash is collected or "ills are paid. ?ote that this wa! is notnecessaril! correct( its the wa! accountants ha%e chosen to do it.

3. The "ottom line num"er shows the change in the cash "alance on the "alance sheet. )s such, it is nota useful num"er for anal!ing a compan!.

4. The ma:or difference is the treatment of interest e#pense. The accounting statement of cash flowstreats interest as an operating cash flow, while the financial cash flows treat interest as a financingcash flow. The logic of the accounting statement of cash flows is that since interest appears on theincome statement, which shows the operations for the period, it is an operating cash flow. In realit!,interest is a financing e#pense, which results from the compan!s choice of de"t and e&uit!. We willha%e more to sa! a"out this in a later chapter. When comparing the two cash flow statements, thefinancial statement of cash flows is a more appropriate measure of the compan!s performance"ecause of its treatment of interest.

5. $aret %alues can ne%er "e negati%e. Imagine a share of stoc selling for @264. This would meanthat if !ou placed an order for >44 shares, !ou would get the stoc along with a chec for 26,444.5ow man! shares do !ou want to "u!7 $ore generall!, "ecause of corporate and indi%idual"anruptc! laws, net worth for a person or a corporation cannot "e negati%e, impl!ing that lia"ilitiescannot e#ceed assets in maret %alue.

6. ;or a successful compan! that is rapidl! e#panding, for e#ample, capital outla!s will "e large,possi"l! leading to negati%e cash flow from assets. In general, what matters is whether the mone! isspent wisel!, not whether cash flow from assets is positi%e or negati%e.

7. Its pro"a"l! not a good sign for an esta"lished compan! to ha%e negati%e cash flow from assets, "utit would "e fairl! ordinar! for a start*up, so it depends.


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SOLUTIONS

8. ;or e#ample, if a compan! were to "ecome more efficient in in%entor! management, the amount ofin%entor! needed would decline. The same might "e true if the compan! "ecomes "etter at collectingits recei%a"les. In general, an!thing that leads to a decline in ending ?WC relati%e to "eginningwould ha%e this effect. ?egati%e net capital spending would mean more long*li%ed assets wereli&uidated than purchased.

9. If a compan! raises more mone! from selling stoc than it pa!s in di%idends in a particular period,its cash flow to stocholders will "e negati%e. If a compan! "orrows more than it pa!s in interest andprincipal, its cash flow to creditors will "e negati%e.

10. The ad:ustments discussed were purel! accounting changes( the! had no cash flow or maret %alueconse&uences unless the new accounting information caused stocholders to re%alue the deri%ati%es.

$olutions to Questions and %ro&le's

NOTE: All end-of-chapter problems were solved using a spreadsheet. Man problems re!uire multiple

steps. "ue to space and readabilit constraints# when these intermediate steps are included in thissolutions manual# rounding ma appear to have occurred. $owever# the final answer for each problem is

found without rounding during an step in the problem.

%asic

1. To find owners e&uit!, we must construct a "alance sheet as follows0

Aalance SheetC) B9,444 C BD,344?;) 63,444 T >3,>44

'E 77T) B68,444 T F 'E B68,444

We now that total lia"ilities and owners e&uit! T F 'E/ must e&ual total assets of B68,444. Wealso now that T F 'E is e&ual to current lia"ilities plus long*term de"t plus owners e&uit!, soowners e&uit! is0

'E G B68,444 @>3,>44 @ D,344 G B>4,H44

?WC G C) @ C G B9,444 @ D,344 G B44

2. The income statement for the compan! is0

Income StatementSales =96,444

Costs 684,444epreciation 38,444EAIT =64,444Interest >9,444EAT =>D,444Ta#es 39K/ H,44?et income =>6H,>44

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CHAPTER 2 B-

'ne e&uation for net income is0

?et income G i%idends L )ddition to retained earnings

Rearranging, we get0

)ddition to retained earnings G ?et income @ i%idends)ddition to retained earnings G =>6H,>44 @ D,444)ddition to retained earnings G =,>44

3. To find the "oo %alue of current assets, we use0 ?WC G C) @ C. Rearranging to sol%e for currentassets, we get0

C) G ?WC L C G 244M L 6.6$ G 23.>$

The maret %alue of current assets and fi#ed assets is gi%en, so0

Aoo %alue C) G 23.>$ $aret %alue C) G 26.8$

Aoo %alue ?;) G 2D.4$ $aret %alue ?;) G 23.6$Aoo %alue assets G 23.>$ L D.4$ G 2.>$ $aret %alue assets G 26.8$ L 3.6$ G 2H.4$

4. Ta#es G 4.>9294M/ L 4.69269M/ L 4.3D269M/ L 4.3263M @ >44M/Ta#es G 28,64

The a%erage ta# rate is the total ta# paid di%ided "! net income, so0

)%erage ta# rate G 28,64 - 263,444)%erage ta# rate G 36.8HK

The marginal ta# rate is the ta# rate on the ne#t 2> of earnings, so the marginal ta# rate G 3K.

5. To calculate 'C;, we first need the income statement0

Income StatementSales =>3,944Costs 9,D44epreciation >,644EAIT =H,44Interest H84Ta#a"le income =H,664Ta#es 34K/ >,8HH?et income =D,39D

'C; G EAIT L epreciation @ Ta#es'C; G =H,44 L >,644 @ >,8HH'C; G =H,63D

6. ?et capital spending G ?;)end@ ?;)"egL epreciation?et capital spending GD,44,444 @ D,644,444 L 69,444

?et capital spending G>,D69,444

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SOLUTIONS

7. The long*term de"t account will increase "! B8 million, the amount of the new long*term de"t issue.Since the compan! sold >4 million new shares of stoc with a B> par %alue, the common stocaccount will increase "! B>4 million. The capital surplus account will increase "! B>H million, the%alue of the new stoc sold a"o%e its par %alue. Since the compan! had a net income of B million,and paid BD million in di%idends, the addition to retained earnings was B3 million, which willincrease the accumulated retained earnings account. So, the new long*term de"t and stocholders

e&uit! portion of the "alance sheet will "e0

ong*term de"t B H8,444,444

Total long*term de"t B H8,444,444

Shareholders e&uit!

+referred stoc B >8,444,444

Common stoc B> par %alue/ 39,444,444

)ccumulated retained earnings 6,444,444

Capital surplus H9,444,444

Total e&uit! B 6>4,444,444

Total ia"ilities F E&uit! B 68,444,444

8. Cash flow to creditors G Interest paid @ ?et new "orrowingCash flow to creditors G Rs.3D4,444 @ Tend@ T"eg/Cash flow to creditors G Rs.3D4,444 @ Rs.3,>44,444 @ 6,844,444/Cash flow to creditors G Rs.3D4,444 @ 344,444Cash flow to creditors G Rs.D4,444

9. Cash flow to stocholders G i%idends paid @ ?et new e&uit!Cash flow to stocholders G Rs.H44,444 @ NCommonendL )+ISend/ @ Common"egL )+IS"eg/O

Cash flow to stocholders G Rs.H44,444 @ NRs.899,444 L ,H44,444/ @ Rs.864,444 L H,844,444/OCash flow to stocholders G Rs.H44,444 @ Rs.8,D99,444 @ ,H64,444/Cash flow to stocholders G @Rs.639,444

?ote, )+IS is the additional paid*in surplus.

10. Cash flow from assets G Cash flow to creditors L Cash flow to stocholdersG Rs.D4,444 @ 639,444

G @Rs.>9,444

Cash flow from assets G @Rs.>9,444 G 'C; @ Change in ?WC @ ?et capital spending@Rs.>9,444 G 'C; @ @Rs.>H9,444/ @ H4,444

'perating cash flow G @Rs.>9,444 L >H9,444 L H4,444'perating cash flow G Rs.34,444

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&ntermediate

11. a. The accounting statement of cash flows e#plains the change in cash during the !ear. Theaccounting statement of cash flows will "e0

Statement of cash flows

Operations

?et income =>69

epreciation 9

Changes in other current assets 69/

Total cash flow from operations =>9

&nvesting activities

)c&uisition of fi#ed assets =>9/

Total cash flow from in%esting acti%ities =>9/

Financing activities

+roceeds of long*term de"t =4

Current lia"ilities >4

i%idends H9/

Total cash flow from financing acti%ities =39

Change in cash on "alance sheet/ =39

b. Change in ?WC G ?WCend@ ?WC"eg

G C)end@ Cend/ @ C)"eg@ C"eg/ G N=D9 L >D9/ @ 4O @ N=>4 L >64/ @ H4/ G =>64 @ 4

G =94

c. To find the cash flow generated "! the firms assets, we need the operating cash flow, and thecapital spending. So, calculating each of these, we find0

Operating cash flow

?et income =>69

epreciation 9

'perating cash flow =644

?ote that we can calculate 'C; in this manner since there are no ta#es.

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SOLUTIONS

'apital spending

Ending fi#ed assets =694

Aeginning fi#ed assets >94/

epreciation 9

Capital spending =>9

?ow we can calculate the cash flow generated "! the firms assets, which is0

'ash flow from assets

'perating cash flow =644

Capital spending >9/

Change in ?WC 94/

Cash flow from assets =69/

?otice that the accounting statement of cash flows shows a positi%e cash flow, "ut the financialcash flows show a negati%e cash flow. The cash flow generated "! the firms assets is a "etternum"er for anal!ing the firms performance.

12. With the information pro%ided, the cash flows from the firm are the capital spending and the changein net woring capital, so0

'ash flows from the firm

Capital spending B3,444/

)dditions to ?WC >,444/

Cash flows from the firm BD,444/

)nd the cash flows to the in%estors of the firm are0

'ash flows to investors of the firm

Sale of short*term de"t B,444/

Sale of long*term de"t >8,444/

Sale of common stoc 6,444/

i%idends paid 63,444

Cash flows to in%estors of the firm BD,444/

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13. a. The interest e#pense for the compan! is the amount of de"t times the interest rate on the de"t.So, the income statement for the compan! is0

Income StatementSales 2>,444,444Cost of goods sold 344,444

Selling costs 644,444epreciation >44,444EAIT 2D44,444Interest >44,444Ta#a"le income 2344,444Ta#es 39K/ >49,444?et income 2>9,444

b. )nd the operating cash flow is0

'C; G EAIT L epreciation @ Ta#es'C; G 2D44,444 L >44,444 @ >49,444

'C; G 239,444

14. To find the 'C;, we first calculate net income.

Income StatementSales P>D9,444Costs 8H,444epreciation ,444'ther e#penses D,44EAIT PD,>44Interest >9,444Ta#a"le income P36,>44

Ta#es D4K/ >6,8D4?et income P>,6H4

i%idends P8,44)dditions to RE P>4,9H4

a. 'C; G EAIT L epreciation @ Ta#es'C; G PD,>44 L ,444 @ >6,8D4'C; G PD>,6H4

b. C;C G Interest @ ?et new TC;C G P>9,444 @ @PH,944/

C;C G P6>,944

?ote that the net new long*term de"t is negati%e "ecause the compan! repaid part of its long*term de"t.

c. C;S G i%idends @ ?et new e&uit!C;S G P8,44 @ H,D94C;S G P6,694

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SOLUTIONS

d. We now that C;) G C;C L C;S, so0

C;) G P6>,944 L 6,694 G P63,94

C;) is also e&ual to 'C; @ ?et capital spending @ Change in ?WC. We alread! now 'C;.?et capital spending is e&ual to0

?et capital spending G Increase in ?;) L epreciation?et capital spending G P9,444 L ,444?et capital spending G P>6,444

?ow we can use0

C;) G 'C; @ ?et capital spending @ Change in ?WCP63,94 G PD>,6H4 @ >6,444 @ Change in ?WC.

Sol%ing for the change in ?WC gi%es P9,9>4, meaning the compan! increased its ?WC "!P9,9>4.

15. The solution to this &uestion wors the income statement "acwards. Starting at the "ottom0

?et income G i%idends L )ddition to ret. earnings?et income G 244 L D,944?et income G 29,D44

?ow, looing at the income statement0

EAT @ EAT Q Ta# rate/ G ?et income

Recognie that EAT Q ta# rate is simpl! the calculation for ta#es. Sol%ing this for EAT !ields0

EAT G ?I - >@ Ta# rate/EAT G 29,D44 - 4.H9EAT G 28,348

?ow we can calculate0

EAIT G EAT L InterestEAIT G 28,348 L >,H44EAIT G 2,48

The last step is to use0

EAIT G Sales @ Costs @ epreciation2,48 G 26,444 @ >3,444 @ epreciationepreciation G 2H,46

Sol%ing for depreciation, we find that depreciation G 2H,46

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16. The "alance sheet for the compan! loos lie this0

Aalance SheetCash 2>9,444 )ccounts pa!a"le 2D34,444)ccounts recei%a"le >D4,444 ?otes pa!a"le >84,444In%entor! 6H9,444 Current lia"ilities 2H>4,444

Current assets 2984,444 ong*term de"t >,D34,444Total lia"ilities 26,4D4,444

Tangi"le net fi#ed assets 6,44,444Intangi"le net fi#ed assets 64,444 Common stoc 77

)ccumulated ret. earnings >,6D4,444Total assets 2D,644,444 Total lia". F owners e&uit! 2D,644,444

Total lia"ilities and owners e&uit! is0

T F 'E G C L T L Common stoc

Sol%ing for this e&uation for e&uit! gi%es us0

Common stoc G 2D,644,444 @ >,6D4,444 @ 6,4D4,444Common stoc G 264,444

17. The maret %alue of shareholders e&uit! cannot "e ero. ) negati%e maret %alue in this case wouldimpl! that the compan! would pa! !ou to own the stoc. The maret %alue of shareholders e&uit!can "e stated as0 Shareholders e&uit! G $a# NT) @ T/, 4O. So, if T) is DD4,444, e&uit! is e&ualto D4,444, and if T) is 334,444, e&uit! is e&ual to 4. We should note here that while the

maret %alue of e&uit! cannot "e negati%e, the "oo %alue of shareholders e&uit! can "e negati%e.

18. a. Ta#es rowth G 4.>9294M/ L 4.69269M/ L 4.3D2>4M/ G 2>,>94Ta#es Income G 4.>9294M/ L 4.69269M/ L 4.3D269M/ L 4.32639M/ L 4.3D28.>H9$/

G 26,84,444

b. Each firm has a marginal ta# rate of 3DK on the ne#t 2>4,444 of ta#a"le income, despite theirdifferent a%erage ta# rates, so "oth firms will pa! an additional 23,D44 in ta#es.

19. Income StatementSales =894,444C'S H34,444)FS e#penses >64,444epreciation >34,444EAIT =34,444/Interest 89,444

Ta#a"le income =>>9,444/Ta#es 39K/ 4

a. ?et income =>>9,444/

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SOLUTIONS

b. 'C; G EAIT L epreciation @ Ta#es'C; G =34,444/ L >34,444 @ 4'C; G =>44,444

c. ?et income was negati%e "ecause of the ta# deducti"ilit! of depreciation and interest e#pense.5owe%er, the actual cash flow from operations was positi%e "ecause depreciation is a non*cash

e#pense and interest is a financing e#pense, not an operating e#pense.

20. ) firm can still pa! out di%idends if net income is negati%e( it :ust has to "e sure there is sufficientcash flow to mae the di%idend pa!ments.

Change in ?WC G ?et capital spending G ?et new e&uit! G 4. i%en/

Cash flow from assets G 'C; @ Change in ?WC @ ?et capital spendingCash flow from assets G =>44,444 @ 4 @ 4 G =>44,444

Cash flow to stocholders G i%idends @ ?et new e&uit!Cash flow to stocholders G =34,444 @ 4 G =34,444

Cash flow to creditors G Cash flow from assets @ Cash flow to stocholdersCash flow to creditors G =>44,444 @ 34,444Cash flow to creditors G =4,444

Cash flow to creditors is also0

Cash flow to creditors G Interest @ ?et new T

So0

?et new T G Interest @ Cash flow to creditors

?et new T G =89,444 @ 4,444?et new T G =>9,444

21. a. The income statement is0

Income StatementSales B>6,844Cost of good sold >4,D44epreciation >,44EAIT B 944Interest D94Ta#a"le income B 94

Ta#es 3DK/ >?et income B33

b. 'C; G EAIT L epreciation @ Ta#es'C; G B944 L >,44 @ >'C; G B6,383

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c. Change in ?WC G ?WCend@ ?WC"egG C)end@ Cend/ @ C)"eg@ C"eg/

G B3,894 @ 6,>44/ @ B3,644 @ >,844/ G B>,94 @ >,D44 G B394

?et capital spending G ?;)end@ ?;)"egL epreciation

G B,44 @ ,>44 L >,44G B6,944

C;) G 'C; @ Change in ?WC @ ?et capital spendingG B6,383 @ 394 @ 6,944G @BDH

The cash flow from assets can "e positi%e or negati%e, since it represents whether the firm raisedfunds or distri"uted funds on a net "asis. In this pro"lem, e%en though net income and 'C; arepositi%e, the firm in%ested hea%il! in "oth fi#ed assets and net woring capital( it had to raise a netBDH in funds from its stocholders and creditors to mae these in%estments.

d. Cash flow to creditorsG Interest @ ?et new TG BD94 @ 4G BD94

Cash flow to stocholders G Cash flow from assets @ Cash flow to creditorsG @BDH @ D94G @B>

We can also calculate the cash flow to stocholders as0

Cash flow to stocholders G i%idends @ ?et new e&uit!

Sol%ing for net new e&uit!, we get0

?et new e&uit! G B944 @ @>/G B>,D>

The firm had positi%e earnings in an accounting sense ?I 4/ and had positi%e cash flow fromoperations. The firm in%ested B394 in new net woring capital and B6,944 in new fi#ed assets. Thefirm had to raise BDH from its staeholders to support this new in%estment. It accomplished this "!raising B>,D> in the form of new e&uit!. )fter pa!ing out B944 of this in the form of di%idends toshareholders and BD94 in the form of interest to creditors, BDH was left to meet the firms cashflow needs for in%estment.

22. a. Total assets 644H G =H94 L 6,44 G =3,994Total lia"ilities 644H G =6H9 L >,944 G =>,H9'wners e&uit! 644H G =3,994 @ >,H9 G =>,89

Total assets 644 G =49 L 3,D44 G =D,>49Total lia"ilities 644 G =64 L >,64 G =6,4>4'wners e&uit! 644 G =D,>49 @ 6,4>4 G =6,49

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SOLUTIONS

b. ?WC 644H G C)4H @ C4H G =H94 @ 6H9 G =389?WC 644 G C)4 @ C4 G =49 @ 64 G =D>9Change in ?WC G ?WC4 @ ?WC4H9 G =D>9 @ 389 G =34

c. We can calculate net capital spending as0

?et capital spending G ?et fi#ed assets 644 @ ?et fi#ed assets 644H L epreciation?et capital spending G =3,D44 @ 6,44 L 844?et capital spending G =>,344

So, the compan! had a net capital spending cash flow of =>,344. We also now that net capitalspending is0

?et capital spending G ;i#ed assets "ought @ ;i#ed assets sold=>,344 G =>,944 @ ;i#ed assets sold;i#ed assets sold G =>,944 @ >,344 G =644

To calculate the cash flow from assets, we must first calculate the operating cash flow. The

operating cash flow is calculated as follows !ou can also prepare a traditional incomestatement/0

EAIT G Sales @ Costs @ epreciationEAIT G =8,H44 @ D,>94 @ 844EAIT G =3,H94

EAT G EAIT @ InterestEAT G =3,H94 @ 6>HEAT G =3,D3D

Ta#es G EAT .39

Ta#es G =3,D3D .39Ta#es G =>,646

'C; G EAIT L epreciation @ Ta#es'C; G =3,H94 L 844 @ >,646'C; G =3,6D8

Cash flow from assets G 'C; @ Change in ?WC @ ?et capital spending.Cash flow from assets G =3,6D8 @ 34 @ >,344Cash flow from assets G =>,>8

d. ?et new "orrowing G T4 @ T4H

?et new "orrowing G =>,64 @ >,944?et new "orrowing G =664

Cash flow to creditors G Interest @ ?et new TCash flow to creditors G =6>H @ 664Cash flow to creditors G @=D

?et new "orrowing G =664 G e"t issued @ e"t retirede"t retired G =344 @ 664 G =84

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23.

Aalance sheet as of ec. 3>, 644H

Cash 26,>4 )ccounts pa!a"le 26,6>3

)ccounts recei%a"le 6,8 ?otes pa!a"le D4

In%entor! D,9 Current lia"ilities 26,H64

Current assets 2,899

ong*term de"t 2,49H

?et fi#ed assets 2>,HH 'wners e&uit! 2>,8D8

Total assets 26,96D Total lia". F e&uit! 26,96D

Aalance sheet as of ec. 3>, 644

Cash 26,>99 )ccounts pa!a"le 26,>DH

)ccounts recei%a"le 3,>D6 ?otes pa!a"le 386

In%entor! 9,4H Current lia"ilities 26,968

Current assets 2>4,33

ong*term de"t 28,636

?et fi#ed assets 2>8,4> 'wners e&uit! 2>,6D

Total assets 268,D8D Total lia". F e&uit! 268,D8D

644H Income Statement 644 Income StatementSales 2D,4>8.44 Sales 2D,3>6.44C'S >,386.44 C'S >,9H.44'ther e#penses 368.44 'ther e#penses 6D.44epreciation 9.44 epreciation 98.44EAIT 2>,3>.44 EAIT 2>,8>.44Interest 6H.44 Interest 34.44

EAT 2>,DH6.44 EAT 2>,986.44Ta#es 3DK/ D.48 Ta#es 3DK/ 93.88?et income 2 HD.6 ?et income 2>,4DD.>6

i%idends 2D88.44 i%idends 2936.44)dditions to RE 2DH.6 )dditions to RE 29>6.>6

24. 'C; G EAIT L epreciation @ Ta#es'C; G 2>,8> L 98 @ 93.88'C; G 2>,3>.>6

Change in ?WC G ?WCend@ ?WC"egG C) @ C/end@ C) @ C/"eg

Change in ?WC G 2>4,33 @ 6,968/ @ 2,899 @ 6,H64/Change in ?WC G 2,8H9 @ ,639 G 2H34

?et capital spending G ?;)end@ ?;)"egL epreciation?et capital spending G 2>8,4> @ >,HH L 98?et capital spending G 2>,444

15


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SOLUTIONS

Cash flow from assets G 'C; @ Change in ?WC @ ?et capital spendingCash flow from assets G 2>,3>.>6 @ H34 @ >,444Cash flow from assets G 234>.>6

Cash flow to creditors G Interest @ ?et new T?et new T G Tend@ T"eg

Cash flow to creditors G 234 @ 28,636 @ ,49H/Cash flow to creditors G @28H

?et new e&uit! G Common stocend@ Common stoc"egCommon stoc L Retained earnings G Total owners e&uit!?et new e&uit! G 'E @ RE/end@ 'E @ RE/"eg?et new e&uit! G 'Eend@ 'E"egL RE"eg@ REendREendG RE"egL )dditions to RE

?et new e&uit! G 'Eend@ 'E"egL RE"eg@ RE"egL )dditions to RE/G 'Eend@ 'E"eg@ )dditions to RE

?et new e&uit! G 2>,6D @ >,8D8 @ 9>6.>6 G @2H3H.>6

Cash flow to stocholders G i%idends @ ?et new e&uit!Cash flow to stocholders G 2936 @ @2H3H.>6/Cash flow to stocholders G 2>,>H8.>6

)s a chec, cash flow from assets is 234>.>6.

Cash flow from assets G Cash flow from creditors L Cash flow to stocholdersCash flow from assets G @28H L >,>H8.>6Cash flow from assets G 234>.>6

'hallenge

25. We will "egin "! calculating the operating cash flow. ;irst, we need the EAIT, which can "ecalculated as0

EAIT G ?et income L Current ta#es L eferred ta#es L InterestEAIT G >6 L >>4 L 6> L 9

EAIT G 384

?ow we can calculate the operating cash flow as0

Operating cash flow

Earnings "efore interest and ta#es 384

epreciation >49 Current ta#es >>4/

'perating cash flow 39

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CHAPTER 2 B-

The cash flow from assets is found in the in%esting acti%ities portion of the accounting statement ofcash flows, so0

'ash flow from assets

)c&uisition of fi#ed assets >8

Sale of fi#ed assets 69/ Capital spending >3

The net woring capital cash flows are all found in the operations cash flow section of theaccounting statement of cash flows. 5owe%er, instead of calculating the net woring capital cashflows as the change in net woring capital, we must calculate each item indi%iduall!. oing so, wefind0

Net wor(ing capital cash flow

Cash >D4

)ccounts recei%a"le 3>

In%entories 6D/ )ccounts pa!a"le >/

)ccrued e#penses >4

?otes pa!a"le H/

'ther 6/

?WC cash flow >34

E#cept for the interest e#pense and notes pa!a"le, the cash flow to creditors is found in the financingacti%ities of the accounting statement of cash flows. The interest e#pense from the income statementis gi%en, so0

'ash flow to creditors Interest 9

Retirement of de"t 8D

e"t ser%ice >D>

+roceeds from sale of long*term de"t >6/

Total >6

)nd we can find the cash flow to stocholders in the financing section of the accounting statementof cash flows. The cash flow to stocholders was0

'ash flow to stoc(holders

i%idends D Repurchase of stoc >9

Cash to stocholders >4

+roceeds from new stoc issue D/

Total H4

17


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SOLUTIONS

26. ?et capital spending G ?;)end@ ?;)"egL epreciationG ?;)end@ ?;)"eg/ L epreciation L )"eg/ @ )"egG ?;)end@ ?;)"eg/L )end@ )"egG ?;)endL )end/ @ ?;)"egL )"eg/ G ;)end@ ;)"eg

27. a. The ta# "u""le causes a%erage ta# rates to catch up to marginal ta# rates, thus eliminating the

ta# ad%antage of low marginal rates for high income corporations.

b. )ssuming a ta#a"le income of 2>44,444, the ta#es will "e0

Ta#es G 4.>9294M/ L 4.69269M/ L 4.3D269M/ L 4.32639M/ G 2>>3.M

)%erage ta# rate G 2>>3.M - 2339M G 3DK

The marginal ta# rate on the ne#t dollar of income is 3D percent.

;or corporate ta#a"le income le%els of 2339M to 2>4$, a%erage ta# rates are e&ual to marginalta# rates.

Ta#es G 4.3D2>4$/ L 4.3929$/ L 4.3823.333$/ G 2H,D>H,HH

)%erage ta# rate G 2H,D>H,HH - 2>8,333,33D G 39K

The marginal ta# rate on the ne#t dollar of income is 39 percent. ;or corporate ta#a"le incomele%els o%er 2>8,333,33D, a%erage ta# rates are again e&ual to marginal ta# rates.

c. Ta#es G 4.3D2644M/ G 2H8M G 4.>9294M/ L 4.69269M/ L 4.3D269M/ L U2>44M/(U2>44M/ G 2H8M @ 66.69M G 2D9.9MU G 2D9.9M - 2>44MU G D9.9K

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CHAPTER 3

FINANCIAL STATEMENTS ANALYSISAND LONG-TERM PLANNING


1. Time trend anal!sis gi%es a picture of changes in the compan!s financial situation o%er time.Comparing a firm to itself o%er time allows the financial manager to e%aluate whether some aspectsof the firms operations, finances, or in%estment acti%ities ha%e changed. +eer group anal!sisin%ol%es comparing the financial ratios and operating performance of a particular firm to a set ofpeer group firms in the same industr! or line of "usiness. Comparing a firm to its peers allows thefinancial manager to e%aluate whether some aspects of the firms operations, finances, or in%estmentacti%ities are out of line with the norm, there"! pro%iding some guidance on appropriate actions totae to ad:ust these ratios if appropriate. Aoth allow an in%estigation into what is different a"out acompan! from a financial perspecti%e, "ut neither method gi%es an indication of whether thedifference is positi%e or negati%e. ;or e#ample, suppose a compan!s current ratio is increasing o%ertime. It could mean that the compan! had "een facing li&uidit! pro"lems in the past and is rectif!ingthose pro"lems, or it could mean the compan! has "ecome less efficient in managing its currentaccounts. Similar arguments could "e made for a peer group comparison. ) compan! with a currentratio lower than its peers could "e more efficient at managing its current accounts, or it could "efacing li&uidit! pro"lems. ?either anal!sis method tells us whether a ratio is good or "ad, "othsimpl! show that something is different, and tells us where to loo.

2. If a compan! is growing "! opening new stores, then presuma"l! total re%enues would "e rising.Comparing total sales at two different points in time might "e misleading. Same*store sales controlfor this "! onl! looing at re%enues of stores open within a specific period.

3. The reason is that, ultimatel!, sales are the dri%ing force "ehind a "usiness. ) firms assets,emplo!ees, and, in fact, :ust a"out e%er! aspect of its operations and financing e#ist to directl! orindirectl! support sales. +ut differentl!, a firms future need for things lie capital assets, emplo!ees,in%entor!, and financing are determined "! its future sales le%el.

4. Two assumptions of the sustaina"le growth formula are that the compan! does not want to sell newe&uit!, and that financial polic! is fi#ed. If the compan! raises outside e&uit!, or increases its de"t*e&uit! ratio, it can grow at a higher rate than the sustaina"le growth rate. 'f course, the compan!could also grow faster than its profit margin increases, if it changes its di%idend polic! "! increasing

the retention ratio, or its total asset turno%er increases.


22/558

SOLUTIONS

5. The sustaina"le growth rate is greater than 64 percent, "ecause at a 64 percent growth rate thenegati%e E;? indicates that there is e#cess financing still a%aila"le. If the firm is >44 percent e&uit!financed, then the sustaina"le and internal growth rates are e&ual and the internal growth rate would"e greater than 64 percent. 5owe%er, when the firm has some de"t, the internal growth rate is alwa!sless than the sustaina"le growth rate, so it is am"iguous whether the internal growth rate would "egreater than or less than 64 percent. If the retention ratio is increased, the firm will ha%e more internal

funding sources a%aila"le, and it will ha%e to tae on more de"t to eep the de"t-e&uit! ratio constant,so the E;? will decline. Con%ersel!, if the retention ratio is decreased, the E;? will rise. If theretention rate is ero, "oth the internal and sustaina"le growth rates are ero, and the E;? will rise tothe change in total assets.

6. Common*sie financial statements pro%ide the financial manager with a ratio anal!sis of thecompan!. The common*sie income statement can show, for e#ample, that cost of goods sold as apercentage of sales is increasing. The common*sie "alance sheet can show a firms increasingreliance on de"t as a form of financing. Common*sie statements of cash flows are not calculated fora simple reason0 There is no possi"le denominator.

7. It would reduce the e#ternal funds needed. If the compan! is not operating at full capacit!, it would

"e a"le to increase sales without a commensurate increase in fi#ed assets.

8. R'E is a "etter measure of the compan!s performance. R'E shows the percentage return for the!ear earned on shareholder in%estment. Since the goal of a compan! is to ma#imie shareholderwealth, this ratio shows the compan!s performance in achie%ing this goal o%er the period.

9. The EAIT-)ssets ratio shows the compan!s operating performance "efore interest, ta#es, anddepreciation. This ratio would show how a compan! has controlled costs. While ta#es are a cost, anddepreciation and amortiation can "e considered costs, the! are not as easil! controlled "! compan!management. Con%ersel!, depreciation and amortiation can "e altered "! accounting choices. Thisratio onl! uses costs directl! related to operations in the numerator. )s such, it gi%es a "etter metricto measure management performance o%er a period than does R').

10. ong*term lia"ilities and e&uit! are in%estments made "! in%estors in the compan!, either in theform of a loan or ownership. Return on in%estment is intended to measure the return the compan!earned from these in%estments. Return on in%estment will "e higher than the return on assets for acompan! with current lia"ilities. To see this, realie that total assets must e&ual total de"t and e&uit!,and total de"t and e&uit! is e&ual to current lia"ilities plus long*term lia"ilities plus e&uit!. So, returnon in%estment could "e calculated as net income di%ided "! total assets minus current lia"ilities.

11. +resuma"l! not, "ut, of course, if the product had "een muchless popular, then a similar fate wouldha%e awaited due to lac of sales.

12. Since customers did not pa! until shipment, recei%a"les rose. The firms ?WC, "ut not its cash,

increased. )t the same time, costs were rising faster than cash re%enues, so operating cash flowdeclined. The firms capital spending was also rising. Thus, all three components of cash flow fromassets were negati%el! impacted.

13. ;inancing possi"l! could ha%e "een arranged if the compan! had taen &uic enough action.Sometimes it "ecomes apparent that help is needed onl! when it is too late, again emphasiing theneed for planning.

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CHAPTER 3 B-

14. )ll three were important, "ut the lac of cash or, more generall!, financial resources ultimatel!spelled doom. )n inade&uate cash resource is usuall! cited as the most common cause of small"usiness failure.

15. emanding cash upfront, increasing prices, su"contracting production, and impro%ing financialresources %ia new owners or new sources of credit are some of the options. When orders e#ceed

capacit!, price increases ma! "e especiall! "eneficial.


NOTE: All end-of-chapter problems were solved using a spreadsheet. Man problems re!uire multiplesteps. "ue to space and readabilit constraints# when these intermediate steps are included in this

solutions manual# rounding ma appear to have occurred. $owever# the final answer for each problem isfound without rounding during an step in the problem.

%asic

1. R'E G +$/T)T/E$/

R'E G .486/>.34/>.9/ G >8.HHK

2. The e&uit! multiplier is0

E$ G > L -EE$ G > L >.34 G 6.34

'ne formula to calculate return on e&uit! is0

R'E G R')/E$/R'E G .486.34/ G 64.4>K

R'E can also "e calculated as0

R'E G ?I - TE

So, net income is0

?I G R'ETE/?I G .644>/2964,444/ G 2>4D,496

3. This is a multi*step pro"lem in%ol%ing se%eral ratios. The ratios gi%en are all part of the u +ontIdentit!. The onl! u +ont Identit! ratio not gi%en is the profit margin. If we now the profit margin,we can find the net income since sales are gi%en. So, we "egin with the u +ont Identit!0

R'E G 4.>H G +$/T)T/E$/ G +$/S - T)/> L -E/

Sol%ing the u +ont Identit! for profit margin, we get0

+$ G NR'E/T)/O - N> L -E/S/O+$ G N4.>H/B>,>89/O - N> L >/ B6,44/O G .439>

21


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SOLUTIONS

?ow that we ha%e the profit margin, we can use this num"er and the gi%en sales figure to sol%e fornet income0

+$ G .439> G ?I - S?I G .439>B6,44/ G BD.84

4. )n increase of sales to =63,4D4 is an increase of0

Sales increase G =63,4D4 @ >,644/ - =>,644Sales increase G .64 or 64K

)ssuming costs and assets increase proportionall!, the pro forma financial statements will loo liethis0

+ro forma income statement +ro forma "alance sheet

Sales =63,4D4.44 )ssets = >>>,H44 e"t = 64,D44.44Costs >8,HH4.44 E&uit! D,33D.D8EAIT D,384.44 Total = >>>,H44 Total = D,3D.D8Ta#es 3DK/ >,D8.64?et income = 6,84.84

The pa!out ratio is constant, so the di%idends paid this !ear is the pa!out ratio from last !ear timesnet income, or0

i%idends G =H3.H4 - =6,D4/=6,84.84/i%idends G =>,>9H.36

The addition to retained earnings is0

)ddition to retained earnings G =6,84.84 @ >,>9H.36)ddition to retained earnings G =>,3D.D8

)nd the new e&uit! "alance is0

E&uit! G =6,H44 L >,3D.D8E&uit! G =D,33D.D8

So the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G =>>>,H44 @ D,3D.D8E;? G =>H,8H9.96

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CHAPTER 3 B-

5. The ma#imum percentage sales increase is the sustaina"le growth rate. To calculate the sustaina"legrowth rate, we first need to calculate the R'E, which is0

R'E G ?I - TER'E G V>6,H6,444 - V3,444,444R'E G .>3H

The plow"ac ratio, b, is one minus the pa!out ratio, so0

bG > @ .34bG .4

?ow we can use the sustaina"le growth rate e&uation to get0

Sustaina"le growth rate G R'E Q "/ - N> @ R'E Q "/OSustaina"le growth rate G N.>3H.4/O - N> @ .>3H.4/OSustaina"le growth rate G .>383 or >3.83K

So, the ma#imum !en increase in sales is0

$a#imum increase in sales G V9D,444,444.>383/$a#imum increase in sales G V,DH,6D.6

6. We need to calculate the retention ratio to calculate the sustaina"le growth rate. The retention ratiois0

bG > @ .34bG .4

?ow we can use the sustaina"le growth rate e&uation to get0

Sustaina"le growth rate G R'E Q b/ - N> @ R'E Q b/OSustaina"le growth rate G N.>.4/O - N> @ .>.4/OSustaina"le growth rate G .>93D or >9.3DK

7. We must first calculate the R'E using the u +ont ratio to calculate the sustaina"le growth rate. TheR'E is0

R'E G +$/T)T/E$/R'E G .4H/>.D4/>.94/R'E G >9.HK

The plow"ac ratio is one minus the di%idend pa!out ratio, so0

bG > @ .D4bG .H4

23


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SOLUTIONS

?ow, we can use the sustaina"le growth rate e&uation to get0

Sustaina"le growth rate G R'E Q b/ - N> @ R'E Q b/OSustaina"le growth rate G N.>9H.H4/O - N> @ .>9H.H4/OSustaina"le growth rate G >4.9K

8. )n increase of sales to 29,>6 is an increase of0

Sales increase G 29,>6 @ D,D44/ - 2D,D44Sales increase G .>8 or >8K

)ssuming costs and assets increase proportionall!, the pro forma financial statements will loo liethis0

+ro forma income statement +ro forma "alance sheet

Sales 2 9,>6 )ssets 2 >9,8>6 e"t 2 ,>44Costs 3,>H8 E&uit! H,36D?et income 2 6,46D Total 2 >9,8>6 Total 2 >9,D6D

If no di%idends are paid, the e&uit! account will increase "! the net income, so0

E&uit! G 2D,344 L 6,46DE&uit! G 2H,36D

So the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 2>9,8>6 @ >9,D6D G 2388

9. a. ;irst, we need to calculate the current sales and change in sales. The current sales are ne#t!ears sales di%ided "! one plus the growth rate, so0

Current sales G ?e#t !ears sales - > Lg/Current sales G Rs.DD4,444,444 - > L .>4/Current sales G Rs.D44,444,444

)nd the change in sales is0

Change in sales G Rs.DD4,444,444 @ D44,444,444Change in sales G Rs.D4,444,444

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CHAPTER 3 B-

We can now complete the current "alance sheet. The current assets, fi#ed assets, and short*termde"t are calculated as a percentage of current sales. The long*term de"t and par %alue of stocare gi%en. The plug %aria"le is the additions to retained earnings. So0

)ssets ia"ilities and e&uit!

Current assets Rs.84,444,444 Short*term de"t Rs.H4,444,444

ong*term de"t Rs.>D9,444,444

;i#ed assets 9H4,444,444 Common stoc Rs.94,444,444

)ccumulated retained earnings 389,444,444

Total e&uit! Rs.D39,444,444

Total assets Rs.HD4,444,444 Total lia"ilities and e&uit! Rs.HD4,444,444

b. We can use the e&uation from the te#t to answer this &uestion. The assets-sales and de"t-salesare the percentages gi%en in the pro"lem, so0

E;? G

Sales

)ssetsQ Sales @

Sales

e"tQ Sales @ pQ +ro:ected sales/ Q > @ d/

E;? G .64 L >.D4/ Q Rs.D4,444,444 @ .>9 Q Rs.D4,444,444/ @ N.>6 Q Rs.DD4,444,444/ Q > @ .D4/O

E;? G Rs.6H,364,444

c. The current assets, fi#ed assets, and short*term de"t will all increase at the same percentage assales. The long*term de"t and common stoc will remain constant. The accumulated retainedearnings will increase "! the addition to retained earnings for the !ear. We can calculate theaddition to retained earnings for the !ear as0

?et income G +rofit margin Q Sales?et income G .>6Rs.DD4,444,444/?et income G Rs.96,844,444

The addition to retained earnings for the !ear will "e the net income times one minus thedi%idend pa!out ratio, which is0

)ddition to retained earnings G ?et income> @ d/)ddition to retained earnings G Rs.96,844,444> @ .D4/)ddition to retained earnings G Rs.3>,H84,444

So, the new accumulated retained earnings will "e0

)ccumulated retained earnings G Rs.39,444,444 L 3>,H84,444)ccumulated retained earnings G Rs.D4H,H84,444

25


28/558

SOLUTIONS

The pro forma "alance sheet will "e0


Current assets Rs.88,444,444 Short*term de"t Rs.HH,444,444

ong*term de"t Rs.>D9,444,444

;i#ed assets H>H,444,444 Common stoc Rs.94,444,444

)ccumulated retained earnings D>H,H84,444

Total e&uit! Rs.DHH,H84,444

Total assets Rs.4D,444,444 Total lia"ilities and e&uit! Rs.H,H84,444

The E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G Rs.4D,444,444 @ H,H84,444

E;? G Rs.6H,364,444

10. a. The sustaina"le growth is0

Sustaina"le growth rate Gb

b

R'E*>

R'E

where0

bG Retention ratio G > @ +a!out ratio G .H9

So0

Sustaina"le growth rate G.H9.4894*>

.H9.4894

Sustaina"le growth rate G .4989 or 9.89K

b. It is possi"le for the sustaina"le growth rate and the actual growth rate to differ. If an! of theactual parameters in the sustaina"le growth rate e&uation differs from those used to computethe sustaina"le growth rate, the actual growth rate will differ from the sustaina"le growth rate.Since the sustaina"le growth rate includes R'E in the calculation, this also implies that changesin the profit margin, total asset turno%er, or e&uit! multiplier will affect the sustaina"le growthrate.

c. The compan! can increase its growth rate "! doing an! of the following0

* Increase the de"t*to*e&uit! ratio "! selling more de"t or repurchasing stoc* Increase the profit margin, most liel! "! "etter controlling costs.* ecrease its total assets-sales ratio( in other words, utilie its assets more efficientl!.* Reduce the di%idend pa!out ratio.

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CHAPTER 3 B-

&ntermediate

11. The solution re&uires su"stituting two ratios into a third ratio. Rearranging -T)0

;irm ) ;irm A - T) G .H4 - T) G .D4

T) @ E/ - T) G .H4 T) @ E/ - T) G .D4T) - T)/ @ E - T)/ G .H4 T) - T)/ @ E - T)/ G .D4> @ E - T)/ G .H4 > @ E - T)/ G .D4E - T) G .D4 E - T) G .H4E G .D4T)/ E G .H4T)/

Rearranging R'), we find0

?I - T) G .64 ?I - T) G .34?I G .64T)/ ?I G .34T)/

Since R'E G ?I - E, we can su"stitute the a"o%e e&uations into the R'E formula, which !ields0

R'E G .64T)/ - .D4T)/ G .64 - .D4 G 94K R'E G .34T)/ - .H4 T)/ G .34 - .H4 G 94K

12. +$ G ?I - S G @=>3,>9H - =>D,3>8 G @8.3K

)s long as "oth net income and sales are measured in the same currenc!, there is no pro"lem( in fact,e#cept for some maret %alue ratios lie E+S and AX+S, none of the financial ratios discussed in thete#t are measured in terms of currenc!. This is one reason wh! financial ratio anal!sis is widel! usedin international finance to compare the "usiness operations of firms and-or di%isions across nationaleconomic "orders. The net income in dollars is0

?I G +$ Q Sales

?I G @4.48326H,HH>/ G @263,43

13. a. The e&uation for e#ternal funds needed is0

E;? G

Sales

)ssetsQ Sales @

Sales

e"tQ Sales @ +$ Q +ro:ected sales/ Q > @ d/

where0

)ssets-Sales G V3>,444,444-V38,444,444 G 4.86Sales G Current sales Q Sales growth rate G V38,444,444.64/ G V,H44,444e"t-Sales G V8,444,444-V38,444,444 G .6>49pG ?et income-Sales G V6,4,444-V38,444,444 G .48+ro:ected sales G Current sales Q > L Sales growth rate/ G V38,444,444> L .64/ G VD9,H44,444dG i%idends-?et income G V>,>H,444-V6,4,444 G .D4

so0

E;? G .86 Q V,H44,444/ @ .6>49 Q V,H44,444/ @ .48 Q VD9,H44,444/ Q > @ .D4/E;? G V6,DD,644

27


30/558

SOLUTIONS

b. The current assets, fi#ed assets, and short*term de"t will all increase at the same percentage assales. The long*term de"t and common stoc will remain constant. The accumulated retainedearnings will increase "! the addition to retained earnings for the !ear. We can calculate theaddition to retained earnings for the !ear as0

?et income G +rofit margin Q Sales

?et income G .48VD9,H44,444/?et income G V3,988,444

The addition to retained earnings for the !ear will "e the net income times one minus thedi%idend pa!out ratio, which is0

)ddition to retained earnings G ?et income> @ d/)ddition to retained earnings G V3,988,444> @ .D4/)ddition to retained earnings G V6,>96,844

So, the new accumulated retained earnings will "e0

)ccumulated retained earnings G V>3,444,444 L 6,>96,844)ccumulated retained earnings G V>9,>96,844

The pro forma "alance sheet will "e0


Current assets V>4,844,444 Short*term de"t V,H44,444

ong*term de"t VH,444,444

;i#ed assets 6H,D44,444 Common stoc VD,444,444

)ccumulated retained earnings >9,>96,844

Total e&uit! V>,>96,844

Total assets V3,644,444 Total lia"ilities and e&uit! V3D,96,844

The E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G V3,644,444 @ 3D,96,844E;? G V6,DD,644

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CHAPTER 3 B-

c. The sustaina"le growth is0

Sustaina"le growth rate Gb

b

R'E*>

R'E

where0

R'E G ?et income-Total e&uit! G V6,4,444-V>,444,444 G .>9bG Retention ratio G Retained earnings-?et income G V>,D,444-V6,4,444 G .H4

So0

Sustaina"le growth rate G.H4.>9J*>

.H4.>9J

Sustaina"le growth rate G .>>84 or >>.84K

d. The compan! cannot :ust cut its di%idends to achie%e the forecast growth rate. )s shown "elow,e%en with a ero di%idend polic!, the E;? will still "e V>,4>6,444.


Current assets V>4,844,444 Short*term de"t V,H44,444

ong*term de"t VH,444,444

;i#ed assets 6H,D44,444 Common stoc VD,444,444

)ccumulated retained earnings >H,988,444

Total e&uit! V64,988,444

Total assets V3,644,444 Total lia"ilities and e&uit! V3H,>88,444

The E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G V3,644,444 @ 3H,>88,444E;? G V>,4>6,444

The compan! does ha%e se%eral alternati%es. It can increase its asset utiliation and-or its profitmargin. The compan! could also increase the de"t in its capital structure. This will decrease thee&uit! account, there"! increasing R'E.

14. This is a multi*step pro"lem in%ol%ing se%eral ratios. It is often easier to loo "acward to determinewhere to start. We need recei%a"les turno%er to find da!s sales in recei%a"les. To calculate

recei%a"les turno%er, we need credit sales, and to find credit sales, we need total sales. Since we aregi%en the profit margin and net income, we can use these to calculate total sales as0

+$ G 4.48H G ?I - Sales G 2>3,444 - Sales( Sales G 26,4>>,H68

Credit sales are 4 percent of total sales, so0

Credit sales G 26,4>>,H684.4/ G 2>,D48,>D4

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SOLUTIONS

?ow we can find recei%a"les turno%er "!0

Recei%a"les turno%er G Sales - )ccounts recei%a"le G 2>,D48,>D4 - 2>D3,644 G .83 times

a!s sales in recei%a"les G 3H9 da!s - Recei%a"les turno%er G 3H9 - .83 G 3.>6 da!s

15. The solution to this pro"lem re&uires a num"er of steps. ;irst, remem"er that C) L ?;) G T). So,if we find the C) and the T), we can sol%e for ?;). .642894/ G 2>,464

To find the total assets, we must first find the total de"t and e&uit! from the information gi%en. So,we find the net income using the profit margin0

+$ G ?I - Sales?I G +rofit margin Q Sales G .492D,3>4/ G 2D4.D9

We now use the net income figure as an input into R'E to find the total e&uit!0

R'E G ?I - TETE G ?I - R'E G 2D4.D9 - .6>9 G 2>,4D.D6

?e#t, we need to find the long*term de"t. The long*term de"t ratio is0

ong*term de"t ratio G 4.4 G T - T L TE/

In%erting "oth sides gi%es0

> - 4.4 G T L TE/ - T G > L TE - T/

Su"stituting the total e&uit! into the e&uation and sol%ing for long*term de"t gi%es the following0

> L 2>,4D.D6 - T G >.D6T G 2>,4D.D6 - .D6 G 2D,DD3.HD

?ow, we can find the total de"t of the compan!0

T G C L T G 2894 L D,DD3.HD G 29,63.HD

)nd, with the total de"t, we can find the TFE, which is e&ual to T)0

T) G T L TE G 29,63.HD L >,4D.D6 G 2,>8.4H

)nd finall!, we are read! to sol%e the "alance sheet identit! as0

?;) G T) @ C) G 2,>8.4H @ >,464 G 2H,>8.4H

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16. This pro"lem re&uires !ou to wor "acward through the income statement. ;irst, recognie that?et income G > @ tC/EAT. +lugging in the num"ers gi%en and sol%ing for EAT, we get0

EAT G 2,894 - 4.H4 G 2>3,483.33

?ow, we can add interest to EAIT to get EAIT as follows0

EAIT G EAT L Interest paid G 2>3,483.33 L 6,>48 G 2>9,>>.33

To get EAIT earnings "efore interest, ta#es, and depreciation/, the numerator in the cash co%erageratio, add depreciation to EAIT0

EAIT G EAIT L epreciation G 2>9,>>.33 L >,H8 G 2>H,88.33

?ow, simpl! plug the num"ers into the cash co%erage ratio and calculate0

Cash co%erage ratio G EAIT - Interest G 2>H,88.33 - 26,>48 G 8.4> times

17. The onl! ratio gi%en which includes cost of goods sold is the in%entor! turno%er ratio, so it is the lastratio used. Since current lia"ilities are gi%en, we start with the current ratio0

Current ratio G 3.3 G C) - C G C) - B3D4,444C) G B>,>66,444

.8 G C) @ In%entor!/ - C G B>,>66,444 @ In%entor!/ - B3D4,444In%entor! G C) @ Yuic ratio Q C/In%entor! G B>,>66,444 @ >.8 Q B3D4,444/In%entor! G B9>4,444

In%entor! turno%er G D.6 G C'S - In%entor! G C'S - B9>4,444C'S G B6,>D6,444

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SOLUTIONS

18. Common Common Common* 6449 sie 644H sie "ase !ear

)ssetsCurrent assetsCash = >4,>H8 6.9DK = >4,H83 6.3K >.494H)ccounts recei%a"le 6,>D9 H.K 68,H>3 H.3DK >.49D>

In%entor! 9,36D >D.84K HD,893 >D.3K >.436Total = H,H3 6D.>>K =>4D,D> 63.48K >.4

;i#ed assets?et plant and e&uipment 34D,>H9 9.8K 3D,>H8 H.6K >.>D>D

Total assets = D44,846 >44K = D9>,3> >44K >.>6H4

ia"ilities and 'wners E&uit!Current lia"ilities

)ccounts pa!a"le = 3,>89 >8.6HK = 9,34 >3.>DK 4.8>4D?otes pa!a"le 3,>69 .HK D8,>H8 >4.HK >.63>>

Total =>>6,3>4 68.46K =>4,D 63.8>K 4.94ong*term de"t = 94,444 >6.DK = H6,444 >3.DK >.6D44

'wners e&uit!Common stoc F paid*in surplus = 84,444 >.HK = 84,444 >.3K >.4444)ccumulated retained earnings >98,D6 3.9DK 64>,8D4 DD.6K >.639

Total = 638,D6 9.94K = 68>,8D4 H6.D9K >.>8>8Total lia"ilities and owners e&uit! = D44,846 >44K = D9>,3> >44K >.>6H4

The common*sie "alance sheet answers are found "! di%iding each categor! "! total assets. ;ore#ample, the cash percentage for 6449 is0

=>4,>H8 - =D44,846 G .469D or 6.9DK

This means that cash is 6.9DK of total assets.

The common*"ase !ear answers are found "! di%iding each categor! %alue for 644H "! the samecategor! %alue for 6449. ;or e#ample, the cash common*"ase !ear num"er is found "!0

=>4,H83 - =>4,>H8 G >.494H

19. To determine full capacit! sales, we di%ide the current sales "! the capacit! the compan! is currentl!using, so0

;ull capacit! sales G Ca2D8,444 - .89;ull capacit! sales G Ca29H6,393

So, the dollar growth rate in sales is0

Sales growth G Ca29H6,393 @ D8,444Sales growth G Ca28D,393

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20. To find the new le%el of fi#ed assets, we need to find the current percentage of fi#ed assets to fullcapacit! sales. oing so, we find0

;i#ed assets - ;ull capacit! sales G Ca2D>9,444 - Ca29H6,393;i#ed assets - ;ull capacit! sales G .384

?e#t, we calculate the total dollar amount of fi#ed assets needed at the new sales figure.

Total fi#ed assets G .384Ca2H84,444/Total fi#ed assets G Ca294>,864

The new fi#ed assets necessar! is the total fi#ed assets at the new sales figure minus the current le%elof fi#ed assets.

?ew fi#ed assets G Ca294>,864 @ D>9,444?ew fi#ed assets G Ca28H,864

21. )ssuming costs %ar! with sales and a 64 percent increase in sales, the pro forma income statement

will loo lie this0

T)I +' ST)TI'?ERS +ro ;orma Income Statement

Sales 2 >,48H,444Costs 896,444'ther e#penses >D,D44EAIT 2 6>,H44Interest >,44Ta#a"le income 2 >,44Ta#es39K/ H,H9?et income 2 >6,39

The pa!out ratio is constant, so the di%idends paid this !ear is the pa!out ratio from last !ear timesnet income, or0

i%idends G 2D6,D98-2>4H,>D9/2>6,39/i%idends G 29>,D

)nd the addition to retained earnings will "e0

)ddition to retained earnings G 2>6,39 @ 9>,D)ddition to retained earnings G 2,H>

The new accumulated retained earnings on the pro forma "alance sheet will "e0

?ew accumulated retained earnings G 269,444 L ,H>?ew accumulated retained earnings G 233D,H>

33


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SOLUTIONS

The pro forma "alance sheet will loo lie this0

T)I +' ST)TI'?ERS+ro ;orma Aalance Sheet

)ssets ia"ilities and 'wners E&uit!

Current assets Current lia"ilitiesCash 2 34,444 )ccounts pa!a"le 2 8,444)ccounts recei%a"le 9>,H44 ?otes pa!a"le ,444In%entor! >,644 Total 2 8,444

Total 2 >6,844 ong*term de"t >9H,444;i#ed assets

?et plant and 'wners e&uit!e&uipment D3H,844 Common stoc and

paid*in surplus 2 6>,444Retained earnings 33D,H>

Total 2 399,H>Total lia"ilities and owners

Total assets 2 H4,H44 e&uit! 2 98,H>

So, the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 2H4,H44 @ 98,H>E;? G 2>4,H3

22. ;irst, we need to calculate full capacit! sales, which is0

;ull capacit! sales G 249,444 - .84;ull capacit! sales G 2>,>3>,694

The capital intensit! ratio at full capacit! sales is0

Capital intensit! ratio G ;i#ed assets - ;ull capacit! salesCapital intensit! ratio G 23HD,444 - 2>,>3>,694Capital intensit! ratio G .36>

The fi#ed assets re&uired at full capacit! sales is the capital intensit! ratio times the pro:ected salesle%el0

Total fi#ed assets G .36>2>,48H,444/ G 23D,DD4

So, E;? is0

E;? G 2>6,844 L 3D,DD4/ @ 298,H> G @2H,6>

?ote that this solution assumes that fi#ed assets are decreased sold/ so the compan! has a >44percent fi#ed asset utiliation. If we assume fi#ed assets are not sold, the answer "ecomes0

E;? G 2>6,844 L 3HD,444/ @ 298,H> G @2H6,>H>

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23. The -E ratio of the compan! is0

-E G 2>9H,444 L D,444/ - 268,444-E G .863D

So the new total de"t amount will "e0

?ew total de"t G .863D2399,H>/?ew total de"t G 26D,944.>>

So, the E;? is0

E;? G 2H4,H44 @ 26D,944.>> L 399,H>/ G @2D4,8H>.>>

)n interpretation of the answer is not that the compan! has a negati%e E;?. ooing "ac at+ro"lem 6>, we see that for the same sales growth, the E;? is 2>4,H3. The negati%e num"er in thiscase means the compan! has too much capital. There are two possi"le solutions. ;irst, the compan!can put the e#cess funds in cash, which has the effect of changing the current asset growth rate.

Second, the compan! can use the e#cess funds to repurchase de"t and e&uit!. To maintain thecurrent capital structure, the repurchase must "e in the same proportion as the current capitalstructure.

'hallenge

24. The pro forma income statements for all three growth rates will "e0

T)I +' ST)TI'?ERS+ro ;orma Income Statement

)* + ,alesrowth

/+ ,alesrowth

*+ ,alesrowth

Sales 2>,4D4,94 2>,48H,444 2>,>3>,694Costs 8>H,944 896,444 88,944'ther e#penses >3,844 >D,D44 >9,444EAIT 2 6>4,D94 2 6>,H44 2 668,94Interest >,44 >,44 >,44Ta#a"le income 2 >4,94 2 >,44 2 64,494Ta#es 39K/ HH,H3 H,H9 3,>H8?et income 2 >63,88 2 >6,39 2 >39,883

i%idends 2 D,99 2 9>,D 2 9D,393 )dd to RE D,33 ,H> 8>,934

We will calculate the E;? for the >9 percent growth rate first. )ssuming the pa!out ratio is constant,the di%idends paid will "e0

i%idends G 2D6,D98-2>4H,>D9/2>63,88/i%idends G 2D,99

35


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SOLUTIONS


)ddition to retained earnings G 2>63,88 @ D,99)ddition to retained earnings G 2D,33


?ew accumulated retained earnings G 269,444 L D,33?ew accumulated retained earnings G 233>,33


)*+ ,ales rowth0T)I +' ST)TI'?ERS+ro ;orma Aalance Sheet


Current assets Current lia"ilitiesCash 2 68,94 )ccounts pa!a"le 2 D,94)ccounts recei%a"le D,D94 ?otes pa!a"le ,444In%entor! 8,D44 Total 2 83,94

Total 2 >H9,H44 ong*term de"t >9H,444;i#ed assets

?et plant and 'wners e&uit!e&uipment D>8,H44 Common stoc and

paid*in surplus 2 6>,444Retained earnings 33>,33

Total 2 396,33Total lia"ilities and owners

Total assets 2 98D,644 e&uit! 2 96,>D3

So, the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 298D,644 @ 96,>D3E;? G @2,D3

)t a 64 percent growth rate, and assuming the pa!out ratio is constant, the di%idends paid will "e0




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CHAPTER 3 B-


?ew accumulated retained earnings G 269,444 L ,H>?ew accumulated retained earnings G 233D,H>


/+ ,ales rowth0

T)I +' ST)TI'?ERS +ro ;orma Aalance Sheet







Total assets 2 H4,H44 e&uit! 2 98,H>

So, the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 2H4,H44 @ 98,H>E;? G 2>4,H3


i%idends G 2D6,D98-2>4H,>D9/2>39,883/i%idends G 29D,393


)ddition to retained earnings G 2>39,883 @ 9D,393)ddition to retained earnings G 28>,934


?ew accumulated retained earnings G 269,444 L 8>,934?ew accumulated retained earnings G 2338,934

37


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SOLUTIONS


*+ ,ales rowth0T)I +' ST)TI'?ERS

+ro ;orma Aalance Sheet


Current assets Current lia"ilitiesCash 2 3>,694 )ccounts pa!a"le 2 8>,694)ccounts recei%a"le 93,94 ?otes pa!a"le ,444In%entor! 9,444 Total 2 4,694


?et plant and 'wners e&uit!e&uipment D99,444 Common stoc and

paid*in surplus 2 6>,444Retained earnings 338,934

Total 2 39,934Total lia"ilities and owners

Total assets 2 H39,444 e&uit! 2 H49,84

So, the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 2H39,444 @ H49,84E;? G 26,66>

25. The pro forma income statements for all three growth rates will "e0

T)I +' ST)TI'?ERS+ro ;orma Income Statement

/+ ,ales

rowth

0/+ ,ales

rowth

0*+ ,ales

rowthSales 2>,48H,444 2>,>H,944 2>,66>,94Costs 896,444 63,444 98,944'ther e#penses >D,D44 >9,H44 >H,644EAIT 2 6>,H44 2 63,44 2 6D,494Interest >,44 >,44 >,44Ta#a"le income 2 >,44 2 6>8,644 2 66,394Ta#es 39K/ H,H9 H,34 ,93?et income 2 >6,39 2 >D>,834 2 >D,8

i%idends 2 9>,D 2 9H,36 2 9,>>> )dd to RE ,H> 89,48 88,HH

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CHAPTER 3 B-

9H,444 L D,444/ - 268,444-E G .863D





The total e&uit! on the pro forma "alance sheet will "e0

?ew total e&uit! G 26>,444 L 69,444 L ,H>?ew total e&uit! G 2399,H>

The new total de"t will "e0

?ew total de"t G .863D2399,H>/?ew total de"t G 26D,944

So, the new long*term de"t will "e the new total de"t minus the new short*term de"t, or0

?ew long*term de"t G 26D,944 @ 8,444?ew long*term de"t G 264,944

39


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SOLUTIONS


,ales growth rate 1 /+ and "ebt2E!uit ratio 1 .3405:




Total 2 >6,844 ong*term de"t 64,944;i#ed assets




Total assets 2 H4,H44 e&uit! 2 H94,DH>

So, the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 2H4,H44 @ H94,DH>E;? G @2D4,8H>


i%idends G 2D6,D98-2>4H,>D9/2>D>,834/i%idends G 29H,36


)ddition to retained earnings G 2>D>,834 @ 9H,36)ddition to retained earnings G 289,48

The new total e&uit! on the pro forma "alance sheet will "e0

?ew total e&uit! G 26>,444 L 69,444 L 89,48?ew total e&uit! G 23H3,48


?ew total de"t G .863D23H3,48/?ew total de"t G 2344,D49

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CHAPTER 3 B-


?ew long*term de"t G 2344,D49 @ 3,944?ew long*term de"t G 264H,49

,ales growth rate 1 0/+ and debt2e!uit ratio 1 .3405:



Current assets Current lia"ilitiesCash 2 36,944 )ccounts pa!a"le 2 8D,944)ccounts recei%a"le 99,44 ?otes pa!a"le ,444In%entor! 8,844 Total 2 3,944

Total 2 >8,644 ong*term de"t 64H,49;i#ed assets

?et plant and 'wners e&uit!e&uipment D3,644 Common stoc and

paid*in surplus 2 6>,444Retained earnings 3D6,48

Total 2 3H3,48Total lia"ilities and owners

Total assets 2 HH4,D44 e&uit! 2 HH3,943

So, the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 2HH4,D44 @ HH3,943E;? G @23,>43


i%idends G 2D6,D98-2>4H,>D9/2>D,8/i%idends G 29,>>>


)ddition to retained earnings G 2>D,8 @ 9,>>>)ddition to retained earnings G 288,HH

The new total e&uit! on the pro forma "alance sheet will "e0

?ew total e&uit! G 26>,444 L 69,444 L 88,HH?ew total e&uit! G 23HH,HH

41


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SOLUTIONS


?ew total de"t G .863D23HH,HH/?ew total de"t G 2343,39


?ew long*term de"t G 2343,39 @ H,94?ew long*term de"t G 264H,H4

,ales growth rate 1 0*+ and debt2e!uit ratio 1 .3405:



Current assets Current lia"ilitiesCash 2 33,94 )ccounts pa!a"le 2 8,94)ccounts recei%a"le 98,494 ?otes pa!a"le ,444In%entor! >46,H44 Total 2 H,94

Total 2 >D,D44 ong*term de"t 64H,H4;i#ed assets

?et plant and 'wners e&uit!e&uipment D>,D44 Common stoc and

paid*in surplus 2 6>,444Retained earnings 3D9,HH

Total 2 3HH,HHTotal lia"ilities and owners

Total assets 2 H89,844 e&uit! 2 H4,46D

So the E;? is0

E;? G Total assets @ Total lia"ilities and e&uit!E;? G 2H89,844 @ H4,46DE;? G 2>9,H

26. We must need the R'E to calculate the sustaina"le growth rate. The R'E is0

R'E G +$/T)T/E$/R'E G .4H6/> - >.99/> L 4.3/R'E G .4964 or 9.64K

?ow, we can use the sustaina"le growth rate e&uation to find the retention ratio as0

Sustaina"le growth rate G R'E Q b/ - N> @ R'E Q b/OSustaina"le growth rate G .>D G N.4964"/O - N> @ .4964"/ObG 6.3H

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CHAPTER 3 B-

This implies the pa!out ratio is0

+a!out ratio G > @ b+a!out ratio G > @ 6.3H+a!out ratio G @>.3H

This is a negati%e di%idend pa!out ratio of >3H percent, which is impossi"le. The growth rate is notconsistent with the other constraints. The lowest possi"le pa!out rate is 4, which corresponds toretention ratio of >, or total earnings retention.

The ma#imum sustaina"le growth rate for this compan! is0

$a#imum sustaina"le growth rate G R'E Q b/ - N> @ R'E Q b/O$a#imum sustaina"le growth rate G N.4964>/O - N> @ .4964>/O$a#imum sustaina"le growth rate G .49D or 9.DK

27. We now that E;? is0

E;? G Increase in assets @ )ddition to retained earnings

The increase in assets is the "eginning assets times the growth rate, so0

Increase in assets G ) g

The addition to retained earnings ne#t !ear is the current net income times the retention ratio, timesone plus the growth rate, so0

)ddition to retained earnings G ?I b/> Lg/

)nd rearranging the profit margin to sol%e for net income, we get0

?I G +$S/

Su"stituting the last three e&uations into the E;? e&uation we started with and rearranging, we get0

E;? G )g/ @ +$S/b> Lg/E;? G )g/ @ +$S/b@ N+$S/bOgE;? G @ +$S/bL N) @ +$S/bOg

28. We start with the E;? e&uation we deri%ed in +ro"lem 6 and set it e&ual to ero0

E;? G 4 G @ +$S/bL N) @ +$S/bOg

Su"stituting the rearranged profit margin e&uation into the internal growth rate e&uation, we ha%e0

Internal growth rate G N+$S/bO - N) @ +$S/bO

43


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SOLUTIONS

Since0

R') G ?I - )R') G +$S/ - )

We can su"stitute this into the internal growth rate e&uation and di%ide "oth the numerator and

denominator "! ). This gi%es0

Internal growth rate G ZN+$S/bO - )[ - ZN) @ +$S/bO - )[Internal growth rate G bR')/ - N> @ bR')/O

To deri%e the sustaina"le growth rate, we must realie that to maintain a constant -E ratio with noe#ternal e&uit! financing, E;? must e&ual the addition to retained earnings times the -E ratio0

E;? G -E/N+$S/b> Lg/OE;? G )g/ @ +$S/b> Lg/

Sol%ing for g and then di%iding numerator and denominator "! )0

Sustaina"le growth rate G +$S/b> L -E/ - N) @ +$S/b> L -E /OSustaina"le growth rate G NR')> L -E /bO - N> @ R')> L -E /bOSustaina"le growth rate G bR'E/ - N> @ bR'E/O

29. In the following deri%ations,the su"script 1E refers to end of period num"ers, and the su"script 1Arefers to "eginning of period num"ers. TE is total e&uit! and T) is total assets.

;or the sustaina"le growth rate:

Sustaina"le growth rate G R'EEQ b/ - > @ R'EEQ b/Sustaina"le growth rate G ?I-TEEQ b/ - > @ ?I-TEEQ b/

We multipl! this e&uation "!0

TEE- TEE/

Sustaina"le growth rate G ?I - TEEQ b/ - > @ ?I - TEEQ b/ Q TEE- TEE/Sustaina"le growth rate G ?I Q b/ - TEE@ ?I Q b/

Recognie that the denominator is e&ual to "eginning of period e&uit!, that is0

TEE@ ?I Q b/ G TEA

Su"stituting this into the pre%ious e&uation, we get0

Sustaina"le rate G ?I Q b/ - TEA

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CHAPTER 3 B-

Which is e&ui%alent to0

Sustaina"le rate G ?I - TEA/ Q b

Since R'EAG ?I - TEA

The sustaina"le growth rate e&uation is0

Sustaina"le growth rate G R'EAQ b

;or the internal growth rate0

Internal growth rate G R')EQ b/ - > @ R')EQ b/Internal growth rate G ?I - T)EQ b/ - > @ ?I - T)EQ b/

We multipl! this e&uation "!0

T)E- T)E/

Internal growth rate G ?I - T)EQ b/ - N> @ ?I - T)EQ b/ Q T)E- T)E/OInternal growth rate G ?I Q b/ - T)E@ ?I Q b/

Recognie that the denominator is e&ual to "eginning of period assets, that is0

T)E@ ?I Q b/ G T)A

Su"stituting this into the pre%ious e&uation, we get0

Internal growth rate G ?I Q b/ - T)A

Which is e&ui%alent to0

Internal growth rate G ?I - T)A/ Q b

Since R')AG ?I - T)A

The internal growth rate e&uation is0

Internal growth rate G R')AQ b

30. Since the compan! issued no new e&uit!, shareholders e&uit! increased "! retained earnings.Retained earnings for the !ear were0

Retained earnings G ?I @ i%idendsRetained earnings G =84,444 @ D,444Retained earnings G =3>,444

45


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SOLUTIONS

So, the e&uit! at the end of the !ear was0

Ending e&uit! G =>H9,444 L 3>,444Ending e&uit! G =>H,444

The R'E "ased on the end of period e&uit! is0

R'E G =84,444 - =>H,444R'E G D4.86K

The plow"ac ratio is0

+low"ac ratio G )ddition to retained earnings-?I+low"ac ratio G =3>,444 - =84,444+low"ac ratio G .389 or G 38.9K

8 or >8.K

The R'E "ased on the "eginning of period e&uit! is

R'E G =84,444 - =>H9,444R'E G .D8D8 or D8.D8K

8 or >8.K


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DISCOUNTED CASH FLOW VALUATION


1. )ssuming positi%e cash flows and interest rates, the future %alue increases and the present %aluedecreases.

2. )ssuming positi%e cash flows and interest rates, the present %alue will fall and the future %alue willrise.

3. The "etter deal is the one with e&ual installments.

4. \es, the! should. )+Rs generall! dont pro%ide the rele%ant rate. The onl! ad%antage is that the! areeasier to compute, "ut, with modern computing e&uipment, that ad%antage is not %er! important.

5. ) freshman does. The reason is that the freshman gets to use the mone! for much longer "eforeinterest starts to accrue.

6. Its a reflection of the time %alue of mone!. $)C gets to use the 2944 immediatel!. If $)C usesit wisel!, it will "e worth more than 2>4,444 in thirt! !ears.

7. 'ddl! enough, it actuall! maes it more desira"le since $)C onl! has the right to pa! the full2>4,444 "efore it is due. This is an e#ample of a 1call feature. Such features are discussed at lengthin a later chapter.

8. The e! considerations would "e0 >/ Is the rate of return implicit in the offer attracti%e relati%e toother, similar ris in%estments7 and 6/ 5ow ris! is the in%estment( i.e., how certain are we that wewill actuall! get the =>4,4447 Thus, our answer does depend on who is maing the promise to repa!.

9. The Treasur! securit! would ha%e a somewhat higher price "ecause the Treasur! is the strongest ofall "orrowers.

10. The price would "e higher "ecause, as time passes, the price of the securit! will tend to rise toward2>4,444. This rise is :ust a reflection of the time %alue of mone!. )s time passes, the time untilreceipt of the 2>4,444 grows shorter, and the present %alue rises. In 64>4, the price will pro"a"l! "ehigher for the same reason. We cannot "e sure, howe%er, "ecause interest rates could "e much

higher, or $)Cs financial position could deteriorate. Either e%ent would tend to depress thesecurit!s price.


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SOLUTIONS


NOTE: All-end-of chapter problems were solved using a spreadsheet. Man problems re!uire multiplesteps. "ue to space and readabilit constraints# when these intermediate steps are included in thissolutions manual# rounding ma appear to have occurred. $owever# the final answer for each problem isfound without rounding during an step in the problem.

%asic

1. The simple interest per !ear is0

29,444 Q .4 G 2394

So, after 9 !ears, !ou will ha%e0

2394 Q 9 G 2>,94 in interest.

The total "alance will "e 29,444 L >,94 G 2H,94

With compound interest, we use the future %alue formula0

;X G +X> Lr/t;X G 29,444>.4/9G 2,4>6.H

The difference is0

2,4>6.H @ H,94 G 26H6.H

2. To find the ;X of a lump sum, we use0

;X G +X> L r/t

a. ;X G B>,444>.4H/>4 G B>,4.89b. ;X G B>,444>.4/>4 G B>,H.>9c. ;X G B>,444>.4H/64 G B3,64.>Dd. Aecause interest compounds on the interest alread! earned, the future %alue in part cis more

than twice the future %alue in part a. With compound interest, future %alues grow e#ponentiall!.

3. To find the +X of a lump sum, we use0

+X G ;X - > L r6t

+X G =>9,D9> - >.49/H

G =>>,96.+X G =9>,99 - >.>>/ G =64,>9D.>+X G =88H,43 - >.>H/>8 G =H>,6HH.8+X G =994,>HD - >.>/63 G =>4,4H.68

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CHAPTER 4 B-

4. To answer this &uestion, we can use either the ;X or the +X formula. Aoth will gi%e the same answersince the! are the in%erse of each other. We will use the ;X formula, that is0

;X G +X> L r/t

Sol%ing for r, we get0

rG ;X - +X/> - t@ >

;X G 234 G 26H9> L r/6( rG 234 - 26H9/>-6@ > G .H3K;X G 28H G 23H4> L r/( rG 28H - 23H4/>-@ > G >4.HHK;X G 2>H6,>8> G 23,444> L r/>9( rG 2>H6,>8> - 23,444/>->9@ > G .K;X G 2D83,944 G 2DH,963> L r/34( rG 2D83,944 - 2DH,963/>-34@ > G 8.>6K


;X G +X> L r/t

Sol%ing for t, we get0

tG ln;X - +X/ - ln> L r/

;X G V>,68D,444 G VH69,444 >.4/t( tG lnV>,68D,444- VH69,444/ - ln >.4 G 8.39 !rs;X G VD,3D>,444 G V8>4,444 >.4/t( tG lnVD,3D>,444- V8>4,444/ - ln >.4 G 6D.8> !rs;X G VD46,HH6,444 G V>8,D44,444 >.6>/t( tG lnVD46,HH6,444 - V>8,D44,444/ - ln >.6> G >H.> !rs;X G V>3,D3,444 G V6>,944,444 >.6/t( tG lnV>3,D3,444 - V6>,944,444/ - ln >.6 G 8.64 !rs

6. To find the length of time for mone! to dou"le, triple, etc., the present %alue and future %alue areirrele%ant as long as the future %alue is twice the present %alue for dou"ling, three times as large for

tripling, etc. To answer this &uestion, we can use either the ;X or the +X formula. Aoth will gi%e thesame answer since the! are the in%erse of each other. We will use the ;X formula, that is0

;X G +X> L r/t

Sol%ing for t, we get0

tG ln;X - +X/ - ln> L r/

The length of time to dou"le !our mone! is0

;X G 26 G 2>>.4H/t

tG ln 6 - ln >.4H G >>.4 !ears

The length of time to &uadruple !our mone! is0

;X G 2D G 2>>.4H/ttG ln D - ln >.4H G 63. !ears

49


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SOLUTIONS

?otice that the length of time to &uadruple !our mone! is twice as long as the time needed to dou"le!our mone! the difference in these answers is due to rounding/. This is an important concept oftime %alue of mone!.

7. To find the +X of a lump sum, we use0

+X G ;X - > L r6t

+X G 2844,444,444 - >.49/64G 2>34,698,9.>6


;X G +X> L r/t

Sol%ing for r, we get0

rG ;X - +X/> - t@ >rG 2>4,3>>,944 - 2>6,3,944/>-D@ > G @ D.DHK

?otice that the interest rate is negati%e. This occurs when the ;X is less than the +X.

9. ) consol is a perpetuit!.To find the +X of a perpetuit!, we use the e&uation0

+X G '- r+X G =>64 - .>9+X G =844.44

10. To find the future %alue with continuous compounding, we use the e&uation0

;X G +XeRt

a. ;X G 2>,444e.>69/ G 2>,866.>6b. ;X G 2>,444e.>43/ G 2>,3D.8Hc. ;X G 2>,444e.49>4/ G 2>,HD8.6d. ;X1 2>,444e.48/ G 2>,94.H

11. To sol%e this pro"lem, we must find the +X of each cash flow and add them. To find the +X of alump sum, we use0

+X G ;X - > L r6t

+X]>4K G =>,644 - >.>4 L =H44 - >.>46L =899 - >.>43L =>,D84 - >.>4DG =3,6D4.4>

+X]>8K G =>,644 - >.>8 L =H44 - >.>86L =899 - >.>83L =>,D84 - >.>8DG =6,3>.H>

+X]6DK G =>,644 - >.6D L =H44 - >.6D6L =899 - >.6D3L =>,D84 - >.6DDG =6,D36.D4

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CHAPTER 4 B-

12. To find the +X), we use the e&uation0

+X) G 'Z> @ N>-> L r6Ot[ - r/

)t a 9 percent interest rate0

U]9K0 +X) G D,444ZN> @ >->.49/O - .49 [ G 68,D3>.6

\]9K0 +X) G H,444ZN> @ >->.49/9O - .49 [ G 69,H.8H

)nd at a 66 percent interest rate0

U]66K0 +X) G D,444ZN> @ >->.66/O - .66 [ G >9,>D9.>D

\]66K0 +X) G H,444ZN> @ >->.66/9O - .66 [ G >,>8>.8D

?otice that the +X of Cash flow U has a greater +X at a 9 percent interest rate, "ut a lower +X at a66 percent interest rate. The reason is that U has greater total cash flows. )t a lower interest rate, the

total cash flow is more important since the cost of waiting the interest rate/ is not as great. )t ahigher interest rate, \ is more %alua"le since it has larger cash flows. )t a higher interest rate, these"igger cash flows earl! are more important since the cost of waiting the interest rate/ is so muchgreater.

13. To find the +X), we use the e&uation0

+X) G 'Z> @ N>-> L r6Ot[ - r/

+X)]>9 !rs0 +X) G Rs.3,H44ZN> @ >->.>4/>9O - .>4[ G Rs.6,38>.8

+X)]D4 !rs0 +X) G Rs.3,H44ZN> @ >->.>4/D4O - .>4[ G Rs.39,64D.98

+X)]9 !rs0 +X) G Rs.3,H44ZN> @ >->.>4/9O - .>4[ G Rs.39,>.4

To find the +X of a perpetuit!, we use the e&uation0

+X G '- r+X G Rs.3,H44 - .>4+X G Rs.3H,444.44

?otice that as the length of the annuit! pa!ments increases, the present %alue of the annuit!approaches the present %alue of the perpetuit!. The present %alue of the 9*!ear annuit! and thepresent %alue of the perpetuit! impl! that the %alue toda! of all perpetuit! pa!ments "e!ond 9 !ears

is onl! Rs.68.34.

14. This cash flow is a perpetuit!. To find the +X of a perpetuit!, we use the e&uation0

+X G '- r+X G 2>9,444 - .48 G 2>8,944.44

51


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SOLUT

modern financial management solutions manual

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